Skorokhod Topology and Convergence of Processes

1987 ◽  
pp. 288-347 ◽  
Author(s):  
Jean Jacod ◽  
Albert N. Shiryaev
Keyword(s):  
Skorokhod Topology

Càdlàg Functions

2021 ◽  
pp. 668-698
Author(s):  
James Davidson
Keyword(s):  
Weak Convergence ◽  
Sufficient Conditions ◽  
Unit Interval ◽  
New Techniques ◽  
Partial Sum ◽  
Skorokhod Topology ◽  
The Right

This chapter considers the space D of functions on the unit interval that are continuous on the right and with left limits, known as càdlàg functions. D contains and extends the space C, but is nonseparable under the uniform metric so to work with it calls for new techniques. By defining a new topology for D (the Skorokhod topology), families of measures on D can be constructed and sufficient conditions for weak convergence of partial sum processes specified.

scholarly journals Coalescence theory for a general class of structured populations with fast migration

2011 ◽  
Vol 43 (04) ◽  
pp. 1027-1047 ◽  
Author(s):  
O. Hössjer
Keyword(s):  
Population Size ◽  
General Class ◽  
Population Genetic ◽  
Total Population ◽  
Structured Populations ◽  
Effective Population ◽  
Constant Change ◽  
Skorokhod Topology ◽  
Age Structured ◽  
Dependency Structures

In this paper we study a general class of population genetic models where the total population is divided into a number of subpopulations or types. Migration between subpopulations is fast. Extending the results of Nordborg and Krone (2002) and Sagitov and Jagers (2005), we prove, as the total population sizeNtends to ∞, weak convergence of the joint ancestry of a given sample of haploid individuals in the Skorokhod topology towards Kingman's coalescent with a constant change of time scalec. Our framework includes age-structured models, geographically structured models, and combinations thereof. We also allow each individual to have offspring in several subpopulations, with general dependency structures between the number of offspring of various types. As a byproduct, explicit expressions for the coalescent effective population sizeN/care obtained.

scholarly journals Approximating Multivariate Tempered Stable Processes

2012 ◽  
Vol 49 (1) ◽  
pp. 167-183 ◽  
Author(s):  
Boris Baeumer ◽  
Mihály Kovács
Keyword(s):  
Particle Tracking ◽  
Random Variable ◽  
Normal Random Variable ◽  
Stable Processes ◽  
Lévy Measure ◽  
Simple Method ◽  
Linear Rate ◽  
Skorokhod Topology ◽  
Lower Dimensional ◽  
Random Angle

We give a simple method to approximate multidimensional exponentially tempered stable processes and show that the approximating process converges in the Skorokhod topology to the tempered process. The approximation is based on the generation of a random angle and a random variable with a lower-dimensional Lévy measure. We then show that if an arbitrarily small normal random variable is added, the marginal densities converge uniformly at an almost linear rate, providing a critical tool to assess the performance of existing particle tracking codes.

The Skorokhod topology on space of fuzzy numbers

2000 ◽  
Vol 111 (3) ◽  
pp. 497-501 ◽  
Author(s):  
Sang Yeol Joo ◽  
Yun Kyong Kim
Keyword(s):  
Fuzzy Numbers ◽  
Skorokhod Topology

scholarly journals Approximation of heavy-tailed fractional Pearson diffusions in Skorokhod topology

2020 ◽  
Vol 486 (2) ◽  
pp. 123934
Author(s):  
N.N. Leonenko ◽  
I. Papić ◽  
A. Sikorskii ◽  
N. Šuvak
Keyword(s):  
Skorokhod Topology ◽  
Heavy Tailed

A GENERAL ORNSTEIN–UHLENBECK STOCHASTIC VOLATILITY MODEL WITH LÉVY JUMPS

2016 ◽  
Vol 19 (08) ◽  
pp. 1650044 ◽  
Author(s):  
KARL FRIEDRICH HOFMANN ◽  
THORSTEN SCHULZ
Keyword(s):  
Stochastic Volatility ◽  
Weak Link ◽  
Stochastic Volatility Model ◽  
Market Model ◽  
Volatility Models ◽  
Volatility Model ◽  
Model Extension ◽  
Skorokhod Topology ◽  
Log Price ◽  
Lévy Jumps

We present a general class of stochastic volatility models with jumps where the stochastic variance process follows a Lévy-driven Ornstein–Uhlenbeck (OU) process and the jumps in the log-price process follow a Lévy process. This financial market model is a true extension of the Barndorff-Nielsen–Shephard (BNS) model class and can establish a weak link between log-price jumps and volatility jumps. Furthermore, we investigate the weak-link [Formula: see text]-OU-BNS model as a special case, where we calculate the characteristic function of the logarithmic price in closed form. The classical [Formula: see text]-OU-BNS model can be obtained as a limit of weak-link [Formula: see text]-OU-BNS models in the Skorokhod topology. We highlight that the weak-link property may be a useful model extension in the case of pricing barrier options.

scholarly journals Poisson convergence for point processes on the plane

1985 ◽  
Vol 39 (2) ◽  
pp. 253-269 ◽  
Author(s):  
B. Gail Ivanoff
Keyword(s):  
Poisson Process ◽  
Point Process ◽  
Point Processes ◽  
Sufficient Conditions ◽  
Two Dimensions ◽  
Two Dimensional ◽  
Convergence In Distribution ◽  
Deterministic Function ◽  
Skorokhod Topology

AbstractA compensator is defined for a point process in two dimensions. It is shown that a Poisson process is characterized by a continuous deterministic compensator. Sufficient conditions are given for convergence in distribution of a sequence of two-dimensional point processes in the Skorokhod topology to a Poisson process when the corresponding sequence of compensators converges pointwise in probability to a continuous deterministic function.

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